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I am studying about Transverse Modes formations in optical waveguides.

Q1.

I got an impressions that this is a constuctive interference phenomenon. while waves that have phase difference 2pi*m; for m = 0,1,2,... will have constructive interference and forming modes, other waves that does not fulfill that phase "rule" will interfere each other destructively.

is it a correct understanding?

EDIT: at certain incoming angles $\theta$, constructive interferences happen in the waveguide. this what we call as modes. while at other angle, the interference is destructive.

Q2.

I also got an impressions that there are two ways of explaining it, one from solving the Maxwell Eqs, the other one is by using that phase different rule.

is my conclusion correct that there two ways to explaining it?

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  • $\begingroup$ Huygens' principle allows you to consider all wave phenomena in more than one dimension in terms of interference. The question to ask yourself is "What do I gain by thinking about it this way?". (Not having studied this subject in these terms; nor in decades in any terms, I can't suggest an answer.) $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jul 8, 2019 at 17:41
  • $\begingroup$ hmm..maybe i was not clear. I am not trying to make a new interpretation. that was just my interpretation during studying. to answer your question, I would say "because I do not know the other way". If you know the correct way, I would be happy to learn it. $\endgroup$
    – Codelearner777
    Commented Jul 8, 2019 at 17:44
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    $\begingroup$ in the transverse directions standing waves are formed $\endgroup$
    – user234190
    Commented Jul 8, 2019 at 17:59
  • $\begingroup$ @user47014, yes. that is what I meant. so at certain incoming angle, the wave in the waveguide fullfill phase different rule. it produces a constructive interference. then we a mode from this angle. is it correct understanding? $\endgroup$
    – Codelearner777
    Commented Jul 8, 2019 at 18:22
  • $\begingroup$ @Codelearner777 Standing wave patterns are formed by multiply reflected wave interference $\endgroup$
    – user234190
    Commented Jul 8, 2019 at 18:49

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I am not sure that i understood the Q1 correctly, but if you mean the quantization of frequency(the presence of a dedicated mods) in optical waveguides - it is the consequence of the condition for the appearance of a standing wave.

Q2 As i understand, phase different rule is the consequence of the Maxwell Eqs because exactly this Eqs predicts the electromagnetic waves(and all their properties).

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  • $\begingroup$ I edit my Q1. maybe you would like to take a look. $\endgroup$
    – Codelearner777
    Commented Jul 8, 2019 at 18:07
  • $\begingroup$ I edited my Q1. maybe your would like to take a look. Q2. hmm..ok. I saw in one book, it was discuss by directly using phase different rule while in other book, they used Maxwell's Eqs but did not mentioned those consequences. maybe that is why I thought there two ways to understand it. $\endgroup$
    – Codelearner777
    Commented Jul 8, 2019 at 18:12
  • $\begingroup$ Well then you mean that in the optical waveguides each wave spreads along the closed path(which setted by certain incoming angles θ). And phase "rule" propose that after wave has gone all the way its phase difference should be 2pi*m. As i understand, it is the condition of stationarity of this wave it is not about the constructive interference. $\endgroup$
    – Leiba Goldstein
    Commented Jul 8, 2019 at 18:17

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